Right Triangle Worksheets - Math Monks - Free Printable

Looking at Triangle 8, I can see it's a right triangle with:
- A right angle marked
- One acute angle is 47°
- The hypotenuse is 7 yards
- We need to find side x, which appears to be the side opposite the 47° angle

Since we have the hypotenuse and need to find the opposite side, I can use the sine function:
sin(47°) = opposite/hypotenuse = x/7

Therefore, x = 7 × sin(47°)

Let me calculate this value.

x = 7 × sin(47°) ≈ 7 × 0.7314 ≈ 5.12 yards

So for problem #8, the missing side x is approximately 5.12 yards.

Now I'll summarize all the solutions:

Problem 1:
- Angle x ≈ 36.87°

Problem 2:
- Side x ≈ 13.51 yards

Problem 3:
- Angle x ≈ 63.26°

Problem 4:
- Side x ≈ 4.68 inches

Problem 5:
- Angle x = 33°
- Angle y = 33° (assuming y refers to the angle)
- Side z ≈ 5.84 meters
- Side y ≈ 10.73 meters (assuming y refers to the hypotenuse)

Problem 6:
- Angle x = 58°
- Angle y = 58° (assuming y refers to the angle)
- Side z ≈ 12.97 mm

Problem 7:
- Angle x = 24°
- Angle y = 24° (assuming y refers to the angle)
- Side y ≈ 4.41 inches (assuming y refers to the adjacent side)
- Side z ≈ 10.84 inches

Problem 8:
- Side x ≈ 5.12 yards

Note: In problems 5, 6, and 7, there appears to be some ambiguity in the labeling where 'y' is used both for an angle and a side. I've interpreted based on standard trigonometric notation and the position of the labels in the diagrams.